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There are 5 distinct fruits. How many ways can they be planted into identical fruit plants?

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There are 5 distinct fruits. How many ways can they be planted into identical fruit plants?

(a) 87

(b) 52

(c) 76

(d) 128

This question was posed to me during an online interview.

This intriguing question comes from Counting topic in section Counting of Discrete Mathematics

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Correct answer is (b) 52

Explanation: These fruits can be placed into 1, 2, 3, 4 or 5 fruit plants. The number of distributions of fruits into fruit plants will thus be the sum of Stirling numbers of the second kind: S(5,1) + S(5,2) + S(5,3) + S(5,4) + S(5,5) = 1 + 15 + 25 + 10 + 1 =  52.

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